3 Solutions 44918 1/21/09 4:25 PM Page 121 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •3–1 Determine the force in each cord for equilibrium of the 200-kg crate Cord BC remains horizontal due to the roller at C, and AB has a length of 1.5 m Set y = 0.75 m 2m A y C 121 B Solutions 44918 1/21/09 4:25 PM Page 122 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–2 If the 1.5-m-long cord AB can withstand a maximum force of 3500 N, determine the force in cord BC and the distance y so that the 200-kg crate can be supported 2m A y C 122 B Solutions 44918 1/21/09 4:25 PM Page 123 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–3 If the mass of the girder is Mg and its center of mass is located at point G, determine the tension developed in cables AB, BC, and BD for equilibrium FAB A 45Њ B 30Њ D C G 123 Solutions 44918 1/21/09 4:25 PM Page 124 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *3–4 If cables BD and BC can withstand a maximum tensile force of 20 kN, determine the maximum mass of the girder that can be suspended from cable AB so that neither cable will fail The center of mass of the girder is located at point G FAB A 45Њ B 30Њ D C G 124 Solutions 44918 1/21/09 4:25 PM Page 125 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •3–5 The members of a truss are connected to the gusset plate If the forces are concurrent at point O, determine the magnitudes of F and T for equilibrium Take u = 30° A O kN u 45Њ D B T C kN F 3–6 The gusset plate is subjected to the forces of four members Determine the force in member B and its proper orientation u for equilibrium The forces are concurrent at point O Take F = 12 kN A O kN u 45Њ D B T C F 125 kN Solutions 44918 1/21/09 4:25 PM Page 126 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–7 The towing pendant AB is subjected to the force of 50 kN exerted by a tugboat Determine the force in each of the bridles, BC and BD, if the ship is moving forward with constant velocity D C 30Њ 20Њ B A 50 kN 126 Solutions 44918 1/21/09 4:25 PM Page 127 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *3–8 Members AC and AB support the 300-lb crate Determine the tensile force developed in each member ft ft B C ft A 127 Solutions 44918 1/21/09 4:25 PM Page 128 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •3–9 If members AC and AB can support a maximum tension of 300 lb and 250 lb, respectively, determine the largest weight of the crate that can be safely supported ft ft B C ft A 128 Solutions 44918 1/21/09 4:25 PM Page 129 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–10 The members of a truss are connected to the gusset plate If the forces are concurrent at point O, determine the magnitudes of F and T for equilibrium Take u = 90° y kN F A B u O x C T 3–11 The gusset plate is subjected to the forces of three members Determine the tension force in member C and its angle u for equilibrium The forces are concurrent at point O Take F = kN y kN F A B O u x C T 129 Solutions 44918 1/21/09 4:25 PM Page 130 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *3–12 If block B weighs 200 lb and block C weighs 100 lb, determine the required weight of block D and the angle u for equilibrium u 30Њ A B D 130 C Solutions 44918 1/21/09 4:25 PM Page 175 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher z 3–62 A force of F = 100 lb holds the 400-lb crate in equilibrium Determine the coordinates (0, y, z) of point A if the tension in cords AC and AB is 700 lb each ft ft B C ft A x y F z y 175 Solutions 44918 1/21/09 4:25 PM Page 176 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–63 If the maximum allowable tension in cables AB and AC is 500 lb, determine the maximum height z to which the 200-lb crate can be lifted What horizontal force F must be applied? Take y = ft z ft ft B C ft A x y F z y 176 Solutions 44918 1/21/09 4:25 PM Page 177 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher z *3–64 The thin ring can be adjusted vertically between three equally long cables from which the 100-kg chandelier is suspended If the ring remains in the horizontal plane and z = 600 mm, determine the tension in each cable 0.5 m C 120Њ D 120Њ 120Њ x z A 177 B y Solutions 44918 1/21/09 4:25 PM Page 178 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher z •3–65 The thin ring can be adjusted vertically between three equally long cables from which the 100-kg chandelier is suspended If the ring remains in the horizontal plane and the tension in each cable is not allowed to exceed kN, determine the smallest allowable distance z required for equilibrium 0.5 m C 120Њ D 120Њ 120Њ x z A 178 B y Solutions 44918 1/21/09 4:25 PM Page 179 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–66 The bucket has a weight of 80 lb and is being hoisted using three springs, each having an unstretched length of l0 = 1.5 ft and stiffness of k = 50 lb>ft Determine the vertical distance d from the rim to point A for equilibrium 80 lb A d D 120Њ 120Њ B 179 1.5 ft 120Њ C Solutions 44918 1/21/09 4:25 PM Page 180 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher z 3–67 Three cables are used to support a 900-lb ring Determine the tension in each cable for equilibrium F A ft 120Њ ft D 120Њ 120Њ C x 180 y B Solutions 44918 1/21/09 4:25 PM Page 181 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *3–68 The three outer blocks each have a mass of kg, and the central block E has a mass of kg Determine the sag s for equilibrium of the system A 1m 30Њ 60Њ 30Њ 1m B C s D E 181 Solutions 44918 1/21/09 4:25 PM Page 182 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •3–69 Determine the angle u such that an equal force is developed in legs OB and OC What is the force in each leg if the force is directed along the axis of each leg? The force F lies in the x-y plane The supports at A, B, C can exert forces in either direction along the attached legs z O u x y F = 100 lb B 120Њ 10 ft 120Њ 120Њ C 182 ft A Solutions 44918 1/21/09 4:25 PM Page 183 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–70 The 500-lb crate is hoisted using the ropes AB and AC Each rope can withstand a maximum tension of 2500 lb before it breaks If AB always remains horizontal, determine the smallest angle u to which the crate can be hoisted C u A 3–71 The members of a truss are pin connected at joint O Determine the magnitude of F1 and its angle u for equilibrium Set F2 = kN F B y kN F2 70Њ 30Њ x O u kN 183 F1 Solutions 44918 1/21/09 4:25 PM Page 184 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *3–72 The members of a truss are pin connected at joint O Determine the magnitudes of F1 and F2 for equilibrium Set u = 60° y kN F2 70Њ 30Њ x O u kN 184 F1 Solutions 44918 1/21/09 4:25 PM Page 185 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher •3–73 Two electrically charged pith balls, each having a mass of 0.15 g, are suspended from light threads of equal length Determine the magnitude of the horizontal repulsive force, F, acting on each ball if the measured distance between them is r = 200 mm 50 mm 150 mm A 150 mm –F F r ϭ 200 mm 185 B Solutions 44918 1/21/09 4:25 PM Page 186 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–74 The lamp has a mass of 15 kg and is supported by a pole AO and cables AB and AC If the force in the pole acts along its axis, determine the forces in AO, AB, and AC for equilibrium z A B 4m 6m O 1.5 m 1.5 m x 186 y C 2m Solutions 44918 1/21/09 4:25 PM Page 187 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher z 3–75 Determine the magnitude of P and the coordinate direction angles of F3 required for equilibrium of the particle Note that F3 acts in the octant shown (Ϫ1 ft, Ϫ7 ft, ft) F1 ϭ 360 lb P F2 ϭ 120 lb F3 ϭ 200 lb x 187 20Њ F4 ϭ 300 lb y Solutions 44918 1/21/09 4:26 PM Page 188 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher *3–76 The ring of negligible size is subjected to a vertical force of 200 lb Determine the longest length l of cord AC such that the tension acting in AC is 160 lb Also, what is the force acting in cord AB? Hint: Use the equilibrium condition to determine the required angle u for attachment, then determine l using trigonometry applied to ¢ABC u C 40Њ l A B ft 200 lb •3–77 Determine the magnitudes of F1, F2, and F3 for equilibrium of the particle z F1 60Њ F3 800 lb 135Њ 60Њ P F2 x 188 200 lb y Solutions 44918 1/21/09 4:26 PM Page 189 © 2010 Pearson Education, Inc., Upper Saddle River, NJ All rights reserved This material is protected under all copyright laws as they currently exist No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher 3–78 Determine the force in each cable needed to support the 500-lb load D z ft y ft B C ft ft ft A x 3–79 The joint of a space frame is subjected to four member forces Member OA lies in the x– y plane and member OB lies in the y– z plane Determine the forces acting in each of the members required for equilibrium of the joint z F1 A F3 O 45Њ y B 40Њ F2 x 189 200 lb